Method of measuring ion concentration and apparatus therefor

Abstract: An apparatus for determining the concentration of an analyte ion in the presence of an interfering ion of the same ionic charge comprises a first ion-selective electrode or ISE (3A), sensitive to the analyte, and a second ISE (3B), sensitive to the interferent. To calibrate the apparatus, the first ISE is brought into contact with first, second and third standard solutions, each containing known concentrations of analyte and interferent. Because the ratio of analyte concentration to interferent in the first standard solution is identical to that in the second standard solution but different to that in the third, the Nicholsky-Eisenmann equation is easily solved to yield the standard potential, E ⊖ , the slope α and the sensitivity coefficient K MN for the ISE. Thereafter the analyte concentration can be obtained from measurements of the electrode potentials using the values determined in this way. In a preferred embodiment, the apparatus takes the form of a flow cell, and the method finds particular application in the measurement of Mg2+ in the presence of Ca2+, or NH₄+ in the presence of K+.

Description: This invention relates to a system and a method for measuring ion concentration in a nutrient solution, blood or other various solution. JP-A-01244356 describes an ion concentration measuring system for measuring the concentration of a measuring ion in a sample solution containing the measuring ions and an interfering ion having the same ionic charge number as that of the measuring ion, which comprises: first, second and third standard solutions; a first ion-selective electrode for generating an output potential in response to the measuring ion; a second ion-selective electrode for generating an output potential in response to the interfering ion; means for sequentially contacting the first ion-selective electrode with the first standard solution, the second standard solution and the third standard solution, each containing known concentrations of the measuring ions and the interfering ions; means for calculating a selectivity coefficient of the first ion-selective electrode on the basis of the output potential of the first ion-selective electrode, which has been obtained through the contact thereof with the first, second and third standard solutions; means for contacting the sample solution with the first and second ion-selective electrodes; and means for calculating the concentration of the measuring ion in the sample solution on the basis of the output potentials of the first and second ion-selective electrodes which has been obtained through the contact thereof with the sample solution and the selectivity coefficient which has been obtained from the first arithmetic means. Conventionally, a potentiometric ion sensor such as an ion-selective electrode or an ion-sensitive field effect transistor has been employed for measuring the concentration of an ion to be measured (hereinafter referred to as a measuring ion) in a sample solution. These sensors are adapted to measure the concentration of a measuring ion in a sample solution on the basis of the following Nernst equation (1). E = E° + αlog (a) where E is output potential of the ion sensor in the sample solution, a is the ion activity (concentration) of the measuring ion in the sample solution, α is the slope (sensitivity) and E° is the output potential (constant) in the standard state. Thus, the equation (1) is inherently formulated for the activity, but the activity can be approximated by the concentration of ion. When the measuring ion is a cation, α becomes positive value, and when it is an anion, α becomes negative value. In this case, α and E° are calculated in advance by using two kinds of standard solutions, each having known ion concentration different from each other. The concentration of an measuring ion can be calculated from the output potential of the ion sensor. However, an ion sensor may often be influenced to some extent by the interfering ion present in the sample solution. This is because the ion sensor is not exclusively sensitive to the measuring ion, showing some sensitivity but also sensitive to the interfering ion. Therefore, the output of the ion sensor thus obtained is the total of the outputs from the measuring ion and from the interfering ion. Namely, even if the concentration of an measuring ion in a sample solution is constant, the output potential of the ion sensor to be obtained may become altered when the concentration of the interfering ion is varied. Therefore, when the concentration of an measuring ion is calculated by using the Nernst equation (1), the ion concentration thus calculated may be altered by the influence from the interfering ion even when the concentration of the measuring ion is actually constant, thus setting forth a problem of error in the resultant value. For example, a magnesium ion sensor is susceptible to the interference from calcium ion. In view of solving above problem, there has been proposed Nicholsky-Eisenmanequation (2) shown as follows, which is a modification of Nernst equation (1). E = E° + αlog[a M + ΣK MN (a N ) m/n ] where E° and α are defined in equation (1), a M is the activity (concentration) of an measuring ion M m , K MN is a selectivity coefficient to an interfering ion N n , a N is the activity (concentration) of an interfering ion N n , m and n are the charge numbers of measuring ion and interfering ion respectively, and Σ represents the sum total of terms of ions which interfere with the measuring ion M m . This Nicholsky-Eisenmanequation is inherently formulated for the activity of ion, but it would not set forth any problem even if the activity of ion is approximated by the concentration of ion. As for the method of experimentally determining the selectivity coefficient K MN as defined by the Nicholsky-Eiseman equation, it can be classified into two categories as prescribed in the provision of Japanese Industrial Standard (JIS K 0122), i.e. mixed solution method and separate solution method. In this mixed solution method, the selectivity coefficient is calculated as follows. Namely, the concentration of measuring ion is varied in a solution containing a constant concentration of an interfering ion together with the measuring ion to obtain a curve of the output potential of ion-selective electrode. Then, the tangent of a region of curve indicating a change in the output potential in proportion to the change in the measuring ion concentration is determined without being influenced by the interfering ion, and at the same time the tangent of a region of curve indicating no change of the output potential due to the influence from the interfering ion is determined. Thereafter, the junction of these tangents is determined, and at the same time the concentration of the measuring ion corresponding to the junction is determined. Finally, the selectivity coefficient is calculated from the relationship between the above concentration of the measuring ion and the concentration of the interfering ion. In alternative to the above method, there is a method wherein the concentration of interfering ion is varied in a solution containing a constant concentration of an measuring ion together with the interfering ion, in contrary to the above. Meanwhile, in the separate solution method, the response characteristic of the output potential is measured in an measuring ion solution as well as in an interfering ion solution respectively, and the selectivity coefficient is calculated either from the concentrations of these ions indicating the same output potential to each other, or from the output potentials of these solutions indicating the same ion concentrations to each other. According to these methods, theoretically speaking, the determination of the selectivity coefficient can be made on the basis of three output potentials. However, it is required to make use of additional output potential other than these three output potentials for determining whether or not these three output potentials are of proper locations in the whole potential response curves. Therefore, in the actual experiment for measuring the selectivity coefficient, at least 5 of 6 kinds of standard solutions are required to be used. For example, in the case of mixed solution method, it is required as shown in FIG. 1 to measure two output potentials at the points (G) and (I) in order to determine a potential response curve located on an high ion concentration side and showing an output potential which is proportional to the concentration of an measuring ion. It is also required to measure output potential at the location H for determining whether or not these two points are influenced by an interfering ion. On the other hand, when a potential response curve which is made constant due to the influence from an interfering ion and located on an low ion concentration side is to be determined, it is required to obtain at least two output potentials (A) and (B) for determining whether or not the potential is saturated. Namely, at least five kinds of solutions each having a different ion concentration from one another are required for accurately measuring the selectivity coefficient by means of the mixed solution method. Moreover, when it is rather impossible to expect a specific value of the selectivity coefficient, it is also hardly possible to expect the range of ion concentration, which indicates a region of change in output potential, so that many measuring points have to be set at small intervals in a wide range of ion concentration, i.e. at least five kinds of standard solutions differing in ion concentration from one another are required in the actual operation. On the other hand, in the case of the separate solution method, a total of at least 4 kinds of standard solutions differing in ion concentration from one another, i.e. at least two kinds for obtaining respective potential response curves for the solution of measuring ion, and for the solution of interfering ion. However, even with these methods, there are problems that the response curve measured of an interfering ion solution fails to indicate the same potential slope as that of the response curve measured of measuring ion solution, and that the proportional relationship between the output potential and the concentration of ion on the lower concentration side may be lost, thereby setting forth a possibility that precise selectivity coefficient may not be obtained. Accordingly, in order to carry out precise measurement by using this conventional method, it is required to prepare at least three kinds of solutions for each ion, i.e. a total of 6 kinds of solutions, and at the same time to perform the comparison of potentials at the same ion concentration, or the comparison of ion concentrations at the same potential in the respective linear region of the potential response curve obtained in advance. As explained above, when the conventional mixed solution method and separate solution method are to be employed for determining the selectivity coefficient of an ion-selective electrode against an interfering ion, at least five kinds of solutions are required, and moreover when it is rather impossible to expect a specific value of the selectivity coefficient, much more kinds of solutions are required, thereby making the measuring operation as well as the calculation involved therefor rather troublesome and complicated. The object of the present invention is to provide an ion concentration measuring system which is capable of easily and accurately measuring the concentration of an ion in a solution. Another object of the present invention is to provide a method of easily and accurately measuring the concentration of an ion in a solution. A further object of the invention is to provide an ion concentration measuring system and a method which is capable of eliminating the interference of ions other than a measuring ion. These objectives are achieved by the method of calibrating an ion-selective electrode according to independent claim 14, and by the system and method of measuring the concentration of a measuring ion in a sample solution according to independent claims 1 and 8 respectively. Further, preferred embodiments of the invention are disclosed in the dependent claims. This invention can be more fully understood from the following detailed description when taken in conjunction with the accompanying drawings, in which: Fig. 1 is a graph illustrating a method of determining a selectivity coefficient according to the conventional mixed solution method; Fig. 2 is a graph illustrating a method of determining a selectivity coefficient according to the conventional separate solution method; Fig. 3 is a drawing for illustrating the principle which underlies an embodiment of this invention; Fig. 4 is a block diagram schematically illustrating the ion concentration measuring apparatus according to the embodiment of this invention; Fig. 5 is a flow chart for illustrating the processes of determining a selectivity coefficient in the ion concentration measuring apparatus shown in Fig. 4; Fig. 6 is a flow chart for illustrating the movement of the ion concentration measuring apparatus shown in Fig. 4; Fig. 7 is a schematic view of the embodiment of the ion concentration measuring apparatus wherein another solution measuring system is employed; and Fig. 8 is a graph illustrating the relationships between an ammonium ion concentration as measured with the apparatus shown in Fig. 7 and the ammonium ion concentration in a sample solution, and between an ammonium ion concentration as measured without compensating the influence of an interfering ion, potassium ion, and the ammonium ion concentration in a sample solution. First, this invention will be explained with reference to FIG. 3 about the outline of method of measuring the selectivity coefficient to be employed in an ion concentration measuring apparatus according to an embodiment of this invention. Referring to FIG. 3, in the operation of the ion concentration measuring apparatus according to an embodiment of this invention, three kinds of standard solutions, each containing known concentrations of the measuring ion M z (z represents ionic charge number) to be measured by using an ion-selective electrode and the corresponding interfering ion N z having the same ionic charge number as that of the measuring ion, are prepared. In this case, the concentrations of each of M z and N z are adjusted such that the relational expression of C M(1) /C N(1) = C M(2) /C N(2) ≠ C M(3) /C N(3) is made valid, where C M(1) and C N(1) represent respectively the concentration of M z ion and the concentration of N z ion in a first standard solution, C M(2) and C N(2) represent respectively the concentration of Mz ion and the concentration of N z ion in a second standard solution, and C M(3) and C N(3) represent respectively the concentration of M z ion and the concentration of N z ion in a third standard solution. Then, the ion-selective electrode is rendered to contact with these three kinds of standard solutions to obtain output potentials, and the selectivity coefficient is determined on the basis of these output potentials thus obtained. In this case, three constants of the following Nicholsky-Eisenman equation (2'), i.e. the selectivity coefficient, the potential slope and standard potential can be determined on the basis of the output potentials of the ion-selective electrode, which have been obtained through the contact thereof with the above three kinds of standard solutions, i.e. the first standard solution A, the second standard solution B and the third standard solution C. E = E° + αlog(a M + ΣK MN ·a N ) wherein E°, α, a M , K MN , and a N are defined in equation (2). To be more specific, the concentration of M z ion can be obtained on the basis of the electrode potential equation (calibration curve), the output potential of the ion-selective electrode to be obtained through the contact thereof with a sample solution containing unknown ion concentration, and the concentration of N z ion to be obtained through a separate ion-selective electrode for measuring the interfering ion N z . In this case, it is assumed that the ion-selective electrode for measuring N z ion is not interfered by M z ion. It is preferable for performing more accurate measurement of the selectivity coefficient to adjust the relationship between the M z ion concentration C M(3) and the N z ion concentration C N(3) in the third standard solution so as to meet the condition of C M(3) < C N(3) . It is also possible to simultaneously calibrate the ion-selective electrode for measuring M z ion and the ion-selective electrode for measuring N z ion, i.e. an interfering ion. As mentioned above, it is possible according to the ion concentration measuring apparatus of the embodiment of this invention to determine the selectivity coefficient by using these three kinds of standard solutions wherein the ratio between the concentration of the measuring ion to be measured by the ion-selective electrode and the interfering ion having the same ionic charge number as that of the measuring ion in the first standard solution is made identical to the ratio between the concentration of the measuring ion to be measured by the ion-selective electrode and the interfering ion having the same ionic charge number as that of the measuring ion in the second standard solution, and made different from a ratio between the concentration of the measuring ion to be measured by the ion-selective electrode and the interfering ion having the same ionic charge number as that of the measuring ion in the third standard solution. Namely, it has become possible according to this invention to easily and accurately measure the selectivity coefficient to an interfering ion having the same ionic charge number as that of the measuring ion by using only three kinds of standard solutions. Moreover, even if it is difficult to expect the range of the selectivity coefficient, it is possible to accurately determine the selectivity coefficient by performing only one measuring operation with three standard solutions. Additionally, it has become possible to determine the selectivity coefficient only through a calculation without requiring any graphic processing of output characteristic graph as in the case of the conventional mixed solution method, so that it has become possible to automate quite easily the measurement of the selectivity coefficient. The ion concentration measuring apparatus according to the embodiment of this invention will be further explained with reference to the block diagram shown in FIG. 4. Referring to FIG. 4, three kinds of standard solutions, i.e. a first standard solution 1A, a second standard solution 1B and a third standard solution 1C, and a sample solution S are disposed in the ion concentration measuring apparatus of this embodiment, and three kinds of electrodes, i.e. an M z ion-selective electrode 3A, an N z ion-selective electrode 3B and a reference electrode 5 are immersed into each of these solutions (for example in the first standard solution as shown in FIG. 4). In this case, it is assumed that the N z ion-selective electrode 3B is not interfered by M z ion. Then, a first potentiometric circuit 7A for measuring the potential difference between the M z ion-selective electrode 3A and the reference electrode 5 is disposed. Likewise, a second potentiometric circuit 7B for measuring the potential difference between the N z ion-selective electrode 3B and the reference electrode 5 is disposed. In this case, it is possible to employ such method that the second potentiometric circuit 7B is omitted, connection between the first potentiometric circuit 7A and the M z ion-selective electrode 3A is changed to connection between the first potentiometric circuit 7A and the N z ion-selective electrode 3B, and potential differences between the reference electrode 5 and the ion-selective electrodes 3A and 3B. The first potentiometric circuit 7A and the second potentiometric circuit 7B are connected to a calculation and memory element 9 so as to store therein the potential differences measured respectively by the first potentiometric circuit 7A and the second potentiometric circuit 7B. To this calculation and memory element 9 is connected an input element 11 and an output element 13. The operation of the apparatus shown in FIG. 4 will now be explained below. The M z ion-selective electrode 3A to be interfered by N z ion of the same ionic charge number as that of M z ion, and an N z ion-selective electrode 3B are immersed together with a reference electrode 5 into each of a first standard solution 1A, a second standard solution 1B and a third standard solution 1C to measure the potential differences (the output potential) between the M z ion-selective electrode 3A and the reference electrode 5 by means of the first potentiometric circuit 7A, and between the N z ion-selective electrode 3B and the reference electrode 5 by means of the second potentiometric circuit 7B respectively. Then, on the basis of the potential differences and the known concentrations of standard solutions fed from an input unit 11, the factor (constant) of the calibration curve of each of the ion-selective electrodes 3A and 3B is determined by the calculation and memory unit 9. Then, these three electrodes 3A, 3B and 5 are immersed into a sample solution S containing unknown concentration of ions in the same manner as mentioned above to measure the potential difference therebetween on the basis of which the concentration of each ion is determined by using the calibration curve prepared in advance. In this case, the concentrations of each of M z ion and N z ion are adjusted such that the relational expression of C M(1) /C N(1) = C M(2) /C N(2) ≠ C M(3) /C N(3) is made valid (see FIG. 3), where C M(1) and C N(1) represent respectively the concentration of M z ion and the concentration of N z ion in a first standard solution, C M(2) and C N(2) represent respectively the concentration of M z ion and the concentration of N z ion in a second standard solution, and C M(3) and C N(3) represent respectively the concentration of M z ion and the concentration of N z ion in a third standard solution. Now, the operation of the ion concentration measuring apparatus according to this embodiment will be explained with reference to FIGS. 5 and 6. The flow chart shown in FIG. 5 illustrates a calibration operation for determining the factor of the calibration curve of each of the ion-selective electrode, and FIG. 6 shows the operation of measuring ion concentration of a sample solution. First, the calibration operation will be explained below with reference to FIG. 5. In the step S1, each of the M z ion concentrations and of the N z ion concentrations of a first standard solution 1A, a second standard solution 1B and a third standard solution 1C are fed from the input unit 11 and stored into the calculation and memory unit 9. In the step S3, the washings of the M z ion-selective electrode 3A, N z ion-selective electrode 3B and the reference electrode 5 are performed. In the step S5, the M z ion-selective electrode 3A, N z ion-selective electrode 3B and the reference electrode 5 thus washed in the step S3 are immersed in the first standard solution 1A. In the step S7, the potential differences between the ion-selective electrode 3A and the reference electrode 5, as well as between the ion-selective electrode 3B and the reference electrode 5 are measured, and the resultant data are stored in the calculation and memory unit 9. Then, in the step S9, the washings of the M z ion-selective electrode 3A, N z ion-selective electrode 3B and the reference electrode 5 used in the steps S3, S5 and S7 are performed. In the step S11, the M z ion-selective electrode 3A, N z ion-selective electrode 3B and the reference electrode 5 thus washed in the step S9 are immersed in the second standard solution 1B. In the step S13, the potential differences between the ion-selective electrode 3A and the reference electrode 5, as well as between the ion-selective electrode 3B and the reference electrode 5 are measured, and the resultant data are stored in the calculation and memory unit 9. Then, in the step S15, the washings of the M z ion-selective electrode 3A, N z ion-selective electrode 3B and the reference electrode 5 used in the steps S9, Sll and S13 are performed. In the step S17, the M z ion-selective electrode 3A, N z ion-selective electrode 3B and the reference electrode 5 thus washed in the step S15 are immersed in the third standard solution 1C. In the step S19, the potential differences between the ion-selective electrode 3A and the reference electrode 5, as well as between the ion-selective electrode 3B and the reference electrode 5 are measured, and the resultant data are stored in the calculation and memory unit 9. Further, in the step S21, the washings of the M z ion-selective electrode 3A, N z ion-selective electrode 3B and the reference electrode 5 used in the steps S15, S17 and S19 are performed. Then, in the step S23, the factors of the calibration curve of each of the ion-selective electrodes 3A and 3B are calculated on the basis of the ion concentrations and the potential differences of the first standard solution 1A, the second standard solution 1B and the third standard solution 1C as measured and stored in the calculation and memory unit 9. Next, the operation of the ion concentration measurement will be explained with reference to FIG. 6. In step S31, the M z ion-selective electrode 3A, N z ion-selective electrode 3B and the reference electrode 5 are immersed in the sample solution S. Then, in the step S33, the potential differences between the ion-selective electrode 3A and the reference electrode 5, as well as between the ion-selective electrode 3B and the reference electrode 5 are measured, and the resultant data are stored in the calculation and memory unit 9. In the step S35, the concentrations of the M z ion and N z ion are calculated in the calculation and memory unit 9 on the basis of the factors of the calibration curve of each of the ion-selective electrodes 3A and 3B stored in advance and the potential difference measured in the sample solution S. The concentrations of the M z ion and N z ion are then supplied to an output unit 13 to be displayed thereon. When it is desired to perform more accurate measurement, the procedures shown in FIGS. 5 and 6 are continuously repeated several times. On the other hand, if it is not required to obtain the data of high accuracy, after the calibration operation shown in FIG. 5 is performed once, the operational procedure shown in the flow chart of FIG. 6 may be repeated several times. The order of operating the standard solutions in the calibration procedure shown in FIG. 5 is not necessarily limited to that shown in FIG. 5, but any other order may be adapted. The washing operation as mentioned herein is not restricted to the washing with pure water or other liquid other than the standard solution, but a standard solution to be used for subsequent measurement of potential, or a sample solution may also be employed as a washing liquid in the washing operation. Further, the washing operation shown in FIGS. 5 and 6 may be omitted. This washing operation can be performed at any other steps or places. When it is desired not to measure the concentration of ion in a sample solution, but to measure only the selectivity coefficient of M z ion-selective electrode 3A, the operation of measuring the ion concentration of a sample solution shown in the flow chart of FIG. 6 may be omitted. Further, all operations concerning the N z ion-selective electrode 3B in the calibration operation shown in FIG. 5 can be omitted. In such a case, the factor of a calibration curve as determined through the calibration of such as the selectivity coefficient, potential slope or standard potential can be represented as the step 37. The flow charts shown in FIGS. 5 and 6 represent the operation of an immersing type measuring apparatus shown in FIG. 4. However, if the operation of immersing in the steps S5, S11, S17 and S31 is replaced by the operation of switching a solution in a flow passage by means of a change-over valve, it may become equivalent to the measuring operation of the flow-cell type flow measuring apparatus. The measuring system of the ion-selective electrode is not only applicable to the immersing type shown in FIG. 4, but also applicable to the flow-cell type flow measuring system shown in FIG. 7. According to the embodiment shown in FIG. 7, three kinds of standard solutions, i.e. the first standard solution 1A, the second standard solution 1B and the third standard solution 1C as well as the sample solution S are introduced into each of the ion-selective electrodes via a passage P through the operation of a change-over valve 21. These solutions are sucked by a pump 27 disposed at an intermediate portion of the passage, and discharged into a drain tank 29. The term of ion-selective electrode referred to in the above embodiment is a general term for indicating a potentiometric ion sensor, and includes an ion sensitive field effect transistor (ISFET). In the followings, a method of measuring selectivity coefficient and a method of measuring ion concentration are explained together with the calculating methods therefor. When the output potential (potential difference) of the M z ion-selective electrode 3A to be influenced by the interference from N z ion is represented respectively by E M(1) with respect to the first standard solution 1A, by E M(2) with respect to the second standard solution 1B and by E M(3) with respect to the third standard solution 1C, the potential slope α M of the M z ion-selective electrode 3A, the selectivity coefficient K MN against N z ion and the standard potential E M ° can be determined respectively by the following equations (3), (4) and (5). α M = (E M(1) -E M(2) )/[log(C M(1) )-log(C M(2) )] K MN = C M(3) -C M(2) ·10 (E M(3) - E M(2) /α M C N(3) -C N(2) ·10 (E M(3) -E M(2) /α M E M ° = E M(1) -α M ·log(C M(1) +K MN ·C N(1) ) A calibration curve according to the Nicholsky-Eiseman equation can be formed by using the values of α M , K MN and E M ° determined above. It is also possible to employ, in place of the above equation (4), the following equation (6), which is equivalent to the equation (4). K MN = - C M(1) -C M(3) ·10 (E M(1) -E M(3) )/α M C N(1) -C N(3) ·10 (E M(1) -E M(3) )/α M Meanwhile, a calibration curve of the N z ion-selective electrode 3B, which is not substantially interfered by M z ion, can be formulated according to the Nernst equation by using the values of the output potential E N(1) and E N(2) derived respectively from the standard solutions 1A and 1B. The potential slope aN of the N z ion-selective electrode 3B and the standard potential E N ° can be determined respectively by the following equations (7) and (8). α N = (E N(1) -E N(2) )/[log(C N(1) )-log(C N(2) )] E N ° = E N(1) -α N ·log(C N(1) ) When the output potential of the two ion-selective electrodes in the sample solution are represented respectively by E M(S) and E N(S) , the N z ion concentration C N(S) and the M z ion concentration C M(S) of the sample solution can be determined respectively by the following equations (9) and (10). C N(S) = 10 (E N(S) - E N °)/α M C M(S) = 10 (E M(S) - E M °)/α M -K MN ·C N(S) The calculation result of the above equation (9) can be applied to the value of C N(S) in the equation (10). In the above ion concentration measuring apparatus, NH 4 + ion-selective electrode containing Nonactin as a sensitive material was used as the ion-selective electrode 3A. This NH 4 + ion-selective electrode is subject to the interference of K + ion. In this case, three kinds of standard solutions, i.e. a solution of: C NH4(1) = 5 mmol/l and C K(1) = 5 mmol/l for the first standard solution 1A, a solution of: C NH4(2) = 0.5 mmol/l and C K(2) = 0.5 mmol/l for the second standard solution 1B, and a solution of: C NH4(3) = 0 mmol/l and C K(3) = 0.5 mmol/l for the third standard solution 1C were employed, and the selectivity coefficient K NH4,K against K + ion was measured to obtain the results as shown in Table 1. The values of the selectivity coefficient K NH4,K which were obtained by way of the conventional mixed solution method and the conventional separate solution method are also shown in the Table 1. It will be easily understood from the Table 1 that the value of the selectivity coefficient K NH4,K obtained by way of this invention is almost equal to the values of the selectivity coefficient K NH4,K obtained by using 9 or 10 kinds of solutions in the conventional mixed solution method or the conventional separate solution method. On the other hand, the values obtained by using the minimum of 5 or 6 kinds of solutions in the conventional mixed solution method or the conventional separate solution method quite differs from the values obtained by way of measuring methods according to this invention or according to the conventional method using a many number of solutions. It will be clear from these results that it is possible according to this invention to accurately and promptly determine the selectivity coefficient by using only three kinds of standard solutions. Further, it is not required according to this invention to employ a graphic processing of a graph depicting a potential curve as is required in the conventional methods. Namely, it is possible according to this invention to determine the selectivity coefficient through a simple numerical calculation. Table 2 shows the results of measurement of the selectivity coefficient wherein the NH4 + ion concentration C NH4(3) and the K + ion concentration C K(3) in the third standard solution were altered according to this invention. In this case, the ion concentrations of the first standard solution 1A and the second standard solution 1B were: C NH4(1) = 5 mmol/l and C K(1) = 5 mmol/l; and C NH4(2) = 0.5 mmol/l and C K(2) = 0.5 mmol/l respectively. Ion Concentration of Third Standard Solution Selectivity Coefficient (Measured value) NH 4 + concentration C NH4(3) (mmol/l) K + concentration C K(3) (mmol/l) K NH4,K 0 5 0.17 0.01 5 0.16 0.1 5 0.17 1 5 0.22 6 5 0.08 0.1 1 0.17 0.05 10 0.15 As clear from the results of the Table 2, when the C K(3) was higher than the C NH4(3) , it was possible to obtain more accurate value of the selectivity coefficient. The NH 4 + ion-selective electrode having its selectivity coefficient K NH4,K against K + ion determined was employed together with a K + ion-selective electrode containing Valinomycin as a sensitive material to constitute an ion concentration measuring apparatus shown in FIG. 4. The above-mentioned three kinds of standard solutions were employed to calibrate the NH 4 + ion-selective electrode and the K + ion-selective electrode to formulate calibration expressions as represented by the equations (9) and (10). Then, these two electrodes were immersed into a sample solution containing unknown concentration of ions, thereby measuring outputs, from which the concentration of each ion was determined by applying them to the calibration curve. The results measured of NH 4 + ion concentration were shown in FIG. 8, wherein the sample solutions employed in the experiment contained a constant amount of 5 mmol/l of KCl and a varied amount of 1 to 10 mmol/l of NH 4 Cl. The measurement of ion concentration was also conducted by using Nernst equation including no term of the selectivity coefficient as a calibration curve equation for the NH 4 + ion-selective electrode, the results of the measurement being shown also in FIG. 8. As shown in FIG. 8, the NH 4 + ion concentration as measured by using the selectivity coefficient determined according to this invention was almost the same as the NH 4 + ion concentration of the sample solution, which was compensated of the interference from K + ion. Namely, the measurement error in this case was within ±9%. In another experiment, The Mg 2+ ion-selective electrode containing as a sensitive material N-heptyl-N', N' - bis{8-[[3-(heptylmethylamino)-1,3-dioxypropyl]amino]octyl}-N-methyl-propanediamide, and the Ca 2+ ion-selective electrode containing as a sensitive material bis[di-(n-octylphenyl)phosphate]calcium were employed to constitute an ion concentration measuring apparatus. This Mg 2+ ion-selective electrode is subject to the interference from Ca 2+ . In this case, the Mg 2+ ion-selective electrode was employed as the ion-selective electrode 3A shown in FIG. 4, and, likewise, the Ca 2+ ion-selective electrode was employed as the ion-selective electrode 3B shown in FIG. 4. In this case, three kinds of standard solutions, i.e. a solution of: C Mg(1) = 2 mmol/l and C Ca(1) = 4 mmol/l for the first standard solution 1A, a solution of: C Mg(2) = 0.2 mmol/l and C Ca(2) = 0.4 mmol/l for the second standard solution 1B, and a solution of: C Mg(3) = 0.1 mmol/l and C Ca(3) = 4 mmol/l for the third standard solution 1C were employed. As a result, the selectivity coefficient K Mg,Ca of the Mg 2+ ion-selective electrode against the Ca 2+ ion was found to be 0.15. This value of the selectivity coefficient K Mg,Ca was found to be almost the same as the results obtained from the conventional mixed solution method (9 solutions were used) and from the conventional separate solution method (10 solutions were used). Further, it was found preferable as in the case of NH 4 + ion-selective electrode to make the C Ca(3) higher than the C Mg(3) for obtaining more accurate value of the selectivity coefficient. When Mg 2+ ion concentration was determined by making use of a calibration curve equation according to the Nicholsky-Eisenmanequation having the above obtained value of selectivity coefficient incorporated therein, and of the Ca 2+ ion concentration obtained from the Ca 2+ ion-selective electrode, the error in the measurement of 0.1 to 4 mmol/l MgCl 2 solution (4 mmol/l CaCl 2 being kept constant) was found to be within ±8%. In still another experiment, The NO 3 - ion-selective electrode containing as a sensitive material trioctylmethylammonium nitrate, and the Cl - ion-selective electrode containing as a sensitive material silver chloride were employed to constitute an ion concentration measuring apparatus. This NO 3 - ion-selective electrode is subject to the interference from Cl - . In this case, three kinds of standard solutions, i.e. a solution of: C NO3(1) = 5 mmol/l and C Cl(1) = 10 mmol/l for the first standard solution 1A, a solution of: C NO3(2) = 0.5 mmol/l and C Cl(2) = 1 mmol/l for the second standard solution 1B, and a solution of: C NO3(3) 0.5 mmol/l and C Cl(3) = 10 mmol/l for the third standard solution 1C were employed to measure the selectivity coefficient K NO3,Cl of the NO 3 - ion-selective electrode against the Cl - ion, finding a value of 0.07. When NO 3 - ion was measured by making use of the above obtained value of selectivity coefficient, the error in the measurement of 0.3 to 8 mmol/l KNO 3 solution (10 mmol/l KCl being kept constant) was found to be within ±6%. As explained above, it is possible according to this embodiment of the invention to accurately and easily determine the selectivity coefficient against an interfering ion having the same ionic charge number as that of an measuring ion by using only three kinds of standard solutions. Further, it is possible to accurately measure a selectivity coefficient by performing only one measuring operation. Moreover, it is not required according to this invention to employ a graphic processing of a graph depicting an output potential curve as is required in the conventional methods. Namely, it is possible according to this invention to determine the selectivity coefficient through a simple numerical calculation, so that the measuring apparatus can be easily automated. Additionally, it is possible according to this ion concentration measuring apparatus to simultaneously carry out the calibration of another ion-selective electrode for measuring the concentration of an interfering ion by using above-mentioned standard solutions for measuring the selectivity coefficient, and to compensate the influence of the interfering ion to the ion-selective electrode, thereby making it possible to accurately measure the concentration of the measuring ion.

Claims: An ion concentration measuring system for measuring the concentration of a measuring ion in a sample solution (S) containing the measuring ion and an interfering ion having the same ionic charge number as that of the measuring ion, which comprises: first, second and third standard solutions (1A, 1B, 1C), each containing known concentrations of the measuring ion and the interfering ion; a first ion-selective electrode (3A, 23A) for generating an output potential in response to the measuring ion (M z ); a second ion-selective electrode (3B, 23B) for generating an output potential in response to the interfering ion (N z ); and arithmetic means (7A, 7B, 9) adapted for calculating the concentration of the measuring ion in the sample solution (S) from the output potentials obtained by contacting the first and second ion-selective electrodes with the sample solution (S) on the basis of the Nicholsky-Eisenman equation: E = E 0 +αlog[ a M +Σ K MN ( a N )] where E 0 is the output potential in the standard state, α is the slope, a M is the activity of the measuring ion, K MN is the selectivity coefficient for the interfering ion, and a N is the activity of the interfering ion CHARACTERIZED IN THAT said arithmetic means is further adapted to calculate E 0 , α and K MN from the respective output potentials of the first ion-selective electrode (3A, 23A) obtained through sequential contact thereof with the first, second and third standard solutions, wherein the ratio between the concentration of the measuring ion (M z ) and the interfering ion (N z ) in the first standard solution (1A) is identical to the ratio between the concentrations of the measuring ion and the interfering ion in the second standard solution (1B), and not identical to the ratio between the concentrations of the measuring ion and the interfering ion in the third standard solution (1C). An ion concentration measuring system according to claim 1, characterized in that the concentration of the measuring ion in the third standard solution is lower than the concentration of the interfering ion. An ion concentration measuring system according to claim 1, characterized by further comprising a reference electrode (5), a first potential difference measuring circuit (7A) for measuring a potential difference between the reference electrode and the ion-selective electrode, and a second potential difference measuring circuit (7B) for measuring a potential difference between the reference electrode and another ion-selective electrode, and wherein said arithmetic means include a calculated result storing element (9) connected to the first and second potential difference measuring circuits, and the calculation storing element is adapted to store the known concentrations of the first, second and third standard solutions. An ion concentration measuring system according to claim 1, characterized by further comprising means for flowing the first, second, third standard solutions and the sample solution; a change-over means (21) for changing over the flows of the first, second, third standard solutions and the sample solution; and means for sequentially contacting the first, second, third standard solutions and the sample solution to the first ion-selective electrode (23A) and to the second ion-selective electrode (23B). An ion concentration measuring system according to claim 1, characterized in that the measuring ions (M z ) are magnesium ions, and the interfering ions (N z ) are calcium ions. An ion concentration measuring system according to claim 1, characterized in that the measuring ions (M z ) are ammonium ions, and the interfering ions (N z ) are potassium ions. An ion concentration measuring system according to claim 1, wherein said arithmetic means (7A, 7B, 9) is adapted for calculating factors of calibration curves of the first and second ion-selective electrodes on the basis of the output potentials of the first and second ion-selective electrodes, which have been obtained through the contact thereof with the first, second and third standard solutions, and for calculating the concentration of the measuring ion in the sample solution on the basis of the output potentials of the first and second ion-selective electrodes which have been obtained through the contact thereof with the sample solution and the calibration curves. A method for measuring the concentration of a measuring ion (M z ) in a sample solution (S) containing the measuring ion and an interfering ion (N z ) having the same ionic charge number as that of the measuring ion, which comprises the steps of: contacting the sample solution (S) with a first ion-selective electrode (3A, 23A) to generate an output potential in response to the measuring ion; contacting the sample solution (S) with a second ion-selective electrode (3B, 23B) to generate an output potential in response to the interfering ion; and calculating the concentration of the measuring ion in the sample solution (S) from the output potentials so obtained on the basis of the Nicholsky-Eisenman equation: E = E 0 +αlog[ a M +Σ K MN ( a N )] where E 0 is the output potential in the standard state, α is the slope, a M is the activity of the measuring ion, K MN is the selectivity coefficient for the interfering ion, and a N is the activity of an interfering ion; CHARACTERIZED IN THAT the constants E 0 , α and K MN are determined by: contacting the first ion-selective electrode sequentially with a first standard solution (1A), a second standard solution (1B) and a third standard solution (1C), each containing known concentrations of the measuring ion and the interfering ion, to generate respective output potentials in response to the measuring ion, wherein the ratio between the concentration of the measuring ion (M z ) and the interfering ion (N z ) in the first standard solution (1A) is identical to the ratio between the concentrations of the measuring ion and the interfering ion in the second standard solution (1B), and not identical to the ratio between the concentrations of the measuring ion and the interfering ion in the third standard solution (1C); and calculating E 0 , α and K MN for the first ion-selective electrode from the output potentials so obtained. A method for measuring the concentration of a measuring ion according to claim 8, characterized in that the concentration of the measuring ion in the third standard solution is lower than the concentration of the interfering ion. A method for measuring the concentration of a measuring ion according to claim 8, characterized by further comprising a step of flowing the first, second, third standard solutions (1A, 1B, 1C) and the sample solution (S); a step of changing over the flows of the first, second, third standard solutions and the sample solution; and a step of sequentially contacting the first, second, third standard solutions and the sample solution to the first ion-selective electrode (23A) and to the second ion-selective electrode (23B). A method for measuring the concentration of a measuring ion according to claim 8, characterized in that the measuring ion (M z ) is magnesium ion, and the interfering ion (N z ) is calcium ion. A method for measuring the concentration of a measuring ion according to claim 8, characterized in that the measuring ion (M z ) is ammonium ion, and the interfering ion (N z ) is potassium ion. A method for measuring the concentration of a measuring ion according to claim 8, wherein: a first calculating step calculates factors of calibration curves of the first and second ion-selective electrodes on the basis of the output potentials of the first and second ion-selective electrodes, which have been obtained through the contact thereof with the first, second and third standard solutions; and a second calculating step calculates the concentration of the measuring ion in the sample solution on the basis of the output potentials of the first and second ion-selective electrodes which have been obtained through the contact thereof with the sample solution and the calibration curves which have been obtained from the first calculating step. A method of calibrating an ion-selective electrode (3A) comprising: contacting the electrode sequentially with a first standard solution (1A), a second standard solution (1B) and a third standard solution (1C), each containing known concentrations of the measuring ion and the interfering ion, to generate respective output potentials in response to the measuring ion, wherein the ratio between the concentration of the measuring ion (M z ) and the interfering ion (N z ) in the first standard solution (1A) is identical to the ratio between the concentrations of the measuring ion and the interfering ion in the second standard solution (1B), and not identical to the ratio between the concentrations of the measuring ion and the interfering ion in the third standard solution (1C); and calculating the constants E 0 , α and K MN for the ion-selective electrode from the output potentials so obtained on the basis of the Nicholsky-Eisenman equation: E = E 0 +αlog[ a M +Σ K MN ( a N )] where E 0 is the output potential in the standard state, α is the slope, a M is the activity of the measuring ion, K MN is the selectivity coefficient for the interfering ion, and a N is the activity of an interfering ion.

Inventors: AMEMIYA ISAO, KIKUCHI HIROSHI, SATO NORIKO, AMEMIYA, ISAO, KIKUCHI, HIROSHI, SATO, NORIKO, AMEMIYA, ISAO, C/O INT. P. DIV, K.K.TOSHIBA, KIKUCHI, HIROSHI, C/O INT. P. DIV, K.K.TOSHIBA, SATO, NORIKO, C/O INTELLECTUAL P. DIV, K.K.TOSHIBA
Applicants: TOSHIBA KK, KABUSHIKI KAISHA TOSHIBA
Application year: 1994
Main classification: G01N27
IPC codes: G01N27